The harmonic oscillator is one of the models most
extensively used in both classical and quantum mechanics. The
usefulness and simplicity make this model a subject of lots of
studies. One of the most important aspects of quantum harmonic
oscillator (QHO) is its dynamic algebra i.e. Weyl-Heisenberg
algebra. This algebra appears in many areas of modern theoretical
physics, as an example we notice that the one-dimensional quantum
harmonic oscillator was successfully used in second quantization
formalism [1]}.
